A number of visual aids are often employed in the teaching and study of statistics. These aids range from simple coins to computer generated curves and graphs. A common device specifically designed for statistical modeling is the Quincunx which was invented by Lord Francis Galton in the 1870's.
A Quincunx employs a funnel shaped conduit to direct a dropped ball downwardly into a pinplate. The pinplate includes a number of spaced rows of outwardly extending pins. Each pin is separated from its neighboring pin by a distance slightly greater than the diameter of the dropped ball. As the ball passes downwardly through the pinplate, it bounces off one pin in each row of pins.
Each row of pins represents an independent disturbance or decision point. When the ball hits one of the pins, it can randomly fall to either the right or left side of the pin. Therefore, if the pinplate includes ten rows of pins, a dropped ball would make ten "choices" in direction before it left the pinplate. After passing through the last row of pins, the ball falls into a "stacking" area.
The stacking area comprises a series of vertically extending receiving grooves or slots. As the dropped ball leaves the pinplate, it falls into the slot directly below its exit point from the pinplate. One or more ball-stops are located in the stacking area and function to stop the ball's downward progress. The dropped balls stack up atop the ball-stop(s) and thereby illustrate the distribution which results from the decision path of the balls through the pinplate. The ballstop(s) can be moved to a "release" position which allows the stacked balls to fall into a bottom reservoir.
A Quincunx is often used to demonstrate process capabilities or stacking of tolerances. For example, if ten washers are to be stacked and each washer is picked at random from a supply having equal numbers of washers of two different sizes, there is a large range of possible stack heights. If the two sizes of washers are one-inch and two-inches respectively, and one happens to pick ten one-inch washers, the stack height will be ten inches. If only two-inch washers are picked, the stack height will be 20 inches., Most likely however, the final stack height will be between these extremes. If a large number of washers are picked, approximately one half will be of one size and the other half will be of the other size. For the above example, one would have the greatest probability of picking five, one-inch washers and five, two-inch washers. Therefore, the probable stack height would be fifteen inches.
A Quincunx could be used to illustrate the above example. A single ball would be dropped from the conduit into a pinplate having ten rows of pins. Each row of pins represents one pick of a washer. If the ball falls to the right, this would represent choosing a two-inch washer. If the ball falls to the left, this represents a one-inch washer being chosen.
Below the pinplate would be located ten groves or slots labeled "10" through "20" respectively with the leftmost groove being labeled "10". These grooves would represent the final stack height.
Dropping a large number of balls into the pinplate would simulate an equally large number of attempts at stacking. The balls would stack up in the grooves and illustrate the distribution of probable stack heights. The balls collected in the grooves would eventually fall into a bell-shaped pattern called a "normal" or "Gausslan" distribution. In this example, the top of the curve would most likely be located in the groove marked "15" and this would indicate that the most probable stack height would be 15 inches.
The problem with the prior art Quincunx devices arises when it is desired to change the number of pinrows (rows of pins) used in the pinplate. If, for example, only five washers were to be picked, one would want a pinplate having only five rows of pins. The normal method of accomplishing this change is to replace the pinplate with another having the desired number of pinrows. This requires the user to have a supply of replacement pinplates that have different numbers of pinrows.
The above solution, while workable, poses a number of problems. One is required to purchase and store the additional replacement pinplates. This is especially onerous when a large number of pinplates are needed. Replacing one pinplate with another is a time consuming procedure that is inconvenient during a teaching session. Also, due to the critical placement of the ball receiving slots below the gaps in the bottom pinrow, the pinplate is required to be an exact, tight fit. A major problem arises since pinplates and Quincunxes are commonly made from wood. The wood expands and contracts depending on such factors as wood type, grain pattern and the wood sealing materials that were used. Therefore, the manufacturing tolerances required for the pinplate and the Quincunx hole into which it fits are critical. These tolerances are extremely hard to meet and this sometimes leads to the pinplate being a poor fit and thereby being hard to remove without breakage of the plate or the Quincunx.
Therefore, the present method of providing a measure of versatility to the Quincunx to illustrate changing conditions is unsatisfactory for most situations and effectively limits the use of the device. In addition, the manufacturing time and skill required to make the device is excessive.